Question

11. Solve the following equations, with
0° < 0 < 90°:
(i) sec 0 - 2 tan 0 = 0​

Answer 1

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Answer 2

Answer:

The value of 0 is 30°

Step-by-step explanation:

Given:-

sec 0 - 2 tan 0 = 0

To find:-

Solve the following equations, with

0° < 0 < 90°:

(i) sec 0 - 2 tan 0 = 0

Solution:-

Given that:-

sec 0 - 2 tan 0 = 0

=>(1/Cos 0)-(2Sin 0/Cos 0)=0

=>(1-2Sin 0)/Cos 0=0

=>1-2Sin 0 = 0× Cos 0

=>1-2Sin 0=0

=>1=2 Sin 0

=>2 Sin0=1

=>Sin 0=1/2

=>Sin 0= Sin 30°

=>0=30°

Answer:-

The value of 0 for the given problem is 30°

Check:-

LHS:-sec 0 - 2 tan 0

=> Sec 30° - 2 tan 30°

=>(2/√3)-2(1/√3)

=>(2/√3)-(2/√3)

=>(2-2)/√3

=>0/√3

=>0

=>RHS

LHS=RHS is true for 0=30°

Used formulae:-

• Sec A= 1/ Cos A
• Tan A = Sin A/ Cos A
• Sin 30°= 1/2
• Tan 30°=1/√3
• Sec 30°=2/√3